 If \(G\)  is a random graph, then the upper-triangular entries of \(L(G)\)  and \(Q(G)\)  satisfy the hypotheses of the theorems in Section . Unfortunately, the vertex degrees of a random graph, while not highly correlated, are not independent. The theorems of Section , therefore, do not apply. A result due to Bryc, Dembo and Jiang on spectral measures of large Markov matrices [1]}, however, can likely be adapted to handle this new situation. Lastly, we remark that the Laplacian and signless Laplacian matrices are positive semi-definite and therefore have non-negative eigenvalues. This motivates the following.
